The volume of multimedia traffic (voice, video, image and data) being transmitted across networks, including wireless communication networks, is increasing. To accommodate the increased volume of multimedia traffic, higher throughput, increased reliability, and more efficient use of limited bandwidth is needed. However, wireless communication networks generally have lower bandwidths, harsher time-varying fading characteristics and higher error rates than wired networks. In addition, in some applications, such as military applications, wireless communication networks also need to protect against intentional interference and provide secure transmissions.
Multi-Carrier Modulation (“MCM”) techniques have been used with wireless communication networks to address these needs. MCM divides a data stream into several parallel streams, each at a much lower bit rate, and then modulates these substreams onto their respective subcarriers (as opposed to the conventional single carrier system). MCM systems include Wavelet Packet Modulation (“WPM”) systems. WPM combines multidimensional communications principles and wavelet principles into a multirate wavelet-based modulation format for orthogonally multiplexed communications. WPM minimizes the adverse effects of narrowband and time-impulsive interference by isolating the impact of such interference to the minimal number of atomic signal components. In other words, WPM allows a flexible, custom mapping of the desired signal on the communications channel at the transmitter to avoid a variety of known interference patterns.
In theory, it is possible to find an optimal WPM mapping for any narrowband/impulsive interference combination. However, the number of possible time-frequency mappings escalates rapidly with respect to the number of levels in the WPM filter bank structure. The number of members in the partition set (number of possible mappings) versus the number of filter bank levels proceeds as follows: one level—2 partitions; two levels—5 partitions; three levels—26 partitions; four levels—677 partitions; five levels—458,330 partitions; six levels—over 210 billion partitions; and so forth. This combinatoric explosion poses a challenge to real-time solution searches. Thus, there is a need for efficiently identifying a mapping to avoid detected noise/interference patterns.
One problem in using WPM in a wireless communication network is performing symbol synchronization at the receiver end. Multi-carrier modulation systems are particularly sensitive to symbol sampling time offsets because the spectral overlap of the subcarriers can cause significant adjacent channel interference (“ACI”) when timing jitter is present. These systems use orthogonal filtering to divide the baseband data into orthogonal frequency subchannels. This process can be thought of as splitting the spectrum of a Nyquist pulse, resulting in subchannels that retain the Nyquist pulse shape (only the period is affected). The transitions between complex symbols that are modulated using conventional Fourier techniques are captured by edge detection techniques that exploit the shape and polarity of the received pulses to determine the optimal sampling instants. WPM produces different (dilated) pulse shapes on each subchannel (also referred to as “sub-band”) such that the composite, orthogonally multiplexed signal lacks usable transitions. Inspection of the resultant signal constellation (i.e., eye pattern) after WPM reveals a nearly continuous footprint (i.e., closed eye). Thus, there is a need for providing symbol synchronization that does not rely on edge detection.
Channel coding has been used to improve the error handling performance of wireless networks. Circular Trellis Coded Modulation (“CTCM”) is a channel coding technique that is based on principles of Trellis Coded Modulation (“TCM”) and turbo coding. CTCM is also referred to as Circular Simplex Turbo Block Coded Modulation (“CSTBCM”) and the terms CTCM and CSTBCM are used interchangeably herein. CSTBCM is a block-based error correction coding method that combines simplex signal mapping and a trellis butterfly structure in a clever way to form a circular tail-biting code. The decoding of CSTBCM can be performed using a circular variant of the decoding algorithm (Bahl Cocke Jelinek Raviv—BCJR) commonly used for turbo product codes (“TPC”). However, the shorter block sizes of CSTBCM provide a bit error rate performance competitive with TPC's large code blocks, approaching the Shannon limit but with considerably lower latency (up to 20-fold improvement). Thus, there also is a need for integrating CSTBCM into a system that uses WPM.